There's lots of different finishes. Personally, I use a tile or slab on pads over a felt or cold applied built up roof finish. But there's few reasons why a timber deck couldn't be laid. Do you need access under the decking?
Is there any insualtion and/or ventilation present?
They're all good. Problems occur when things aren't installed properly or products mis-matched.
Does the whole section of roof need to be replaced? Where is the leak? Or is the roofing just at the end of it's life?
If it's the latter then why not renew like for like? If there's a specific leak, what is causing it?
I've recently looked at a new roof over an extension that has all the materials present but not put together with any care – or sense.
Have you asked someone to diagnose the problem or are you just asking for quotes to replace the roof?